Condensed Matter

Topological states of matter are of of fundamental interest in contemporate condensed matter physics. Today, the fractional Quantum Hall effect remains the only known experimental system expected to exhibit intrinsic topological order. The question remains whether also different systems might stabilize this kind of ordering. Chiral spin liquids are an analogue of Fractional Quantum Hall Effect wave functions for spin systems. These wavefunctions have been envisioned in 1987 but only very recently several simple frustrated quantum spin models have been proposed realizing this physics. In this talk we will introduce chiral spin liquids, discuss their relation to the Fractional Quantum Hall effect and present our recent numerical studies that provide conclusive evidence for the emergence of this exotic state of matter in extended frustrated Heisenberg models. In the course of these projects novel algorithms and techniques for large scale Exact Diagonalization were developed and applied. We briefly discuss these techniques and show that they allow for sparse diagonalizations of Heisenberg systems up to 48-50 spin-1/2 particles.

Since its first discovery in 1986, high-Tc superconductors have been attracting constant interests and meticulous efforts from both theorists and experimentalists, not merely due to its large transition temperature, but also because it offers a well characterized laboratory for the study of exotic phenomena such as quantum criticality, non-Fermi liquid behavior, and intertwined orders. One pressing question in the field is the role played by disorder:

inevitable in real materials, disorder is able to fundamentally alter the properties of the system under certain circumstances. In this talk, we will discuss from a theoretical point of view, how different types of disorders affect various electronic orders in copper-based high-Tc superconductors. We also discuss the implications in experiments, and investigate the possibility of generalizing our conclusions to a variety of other physical systems.

Motivated by the question about reconstructing a Conformal field theory from the data of a subfactor of finite index, Jones studied the continuous limit of the periodic quantum spin chain which Thompson group acts on. Based on planar algebras, the topological axiomatization of subfactors, we will illustrate the idea of the correspondence between the skein theory of planar algebras and presentation of Thompson groups.

Bosonic symmetric protected topological (BSPT) phases are bosonic anagolue of electron topological insulators and superconductors. Despite the theoretical progresses of classifying these states, little attention has been paid to experimental realization of BSPT states in dimensions higher than 1. We propose bilayer graphene system in a out-of-plane magnetic field with Coulomb interaction is a natural platform for BSPT states with $U(1)\times U(1)$ symmetry. We also propose that the quantum phase transition between the BSPT state and the trivial state, which may be tuned by an out-of-plane electric field, could be a novel transition with only gapless bosonic degrees of freedom. In the second part of the talk we will discuss the out-of-time-order correlation (OTOC) and its application in many-body localized and marginal MBL systems. We demonstrate, in marginal MBL systems, the scrambling time follows a stretched exponential scaling with the distance between the operators, which demonstrates Sinai diffusion of quantum information and the enhanced scrambling by the quantum criticality in non-chaotic systems.

The matrix product state (MPS) ansatz makes possible computationally-efficient representations of weakly entangled many-body quantum systems with gapped Hamiltonians near their ground states, notably including massive, relativistic quantum fields on the lattice. No Wick rotation is required to apply the time evolution operator, enabling study of time-dependent Hamiltonians. Using free massive scalar field theory on the 1+1 Robertson-Walker metric as a toy example, I present early efforts to exploit this fact to model quantum fields in curved spacetime. We use the ADM formalism to write the appropriate Hamiltonian witnessed by a particular class of normal observers. Possible applications include simulations of gravitational particle production in the presence of interactions, studies of the slicing-dependence of entanglement production, and inclusion of the expectation of the stress-energy tensor as a matter source in a numerical relativity simulation.

Unlike entanglement entropy and mutual information which may mix both classical and quantum correlations, entanglement negativity received extensive interest recently, for its merit of measuring the pure quantum entanglement in the system. In this talk, I will introduce the entanglement negativity in 2+1 dimensional topologically ordered phases. For a bipartitioned or tripartitioned spatial manifold, we show how the universal part of entanglement negativity depends on the presence of quasiparticles and the choice of ground states. Besides interpreting recent results in exactly solvable lattice models, we give new results on non-Abelian topologically ordered phases.

Condensed matter realizations of Majorana zero modes constitute potential building blocks of a topological quantum computer and thus have recently been the subject of intense theoretical and experimental investigation.  In the first part of this talk, I will introduce a new scheme for preparation, manipulation, and readout of these zero modes in semiconducting wires coated with mesoscopic superconducting islands.  This approach synthesizes recent materials growth breakthroughs with tools long successfully deployed in quantum-dot research, notably gate-tunable island couplings, charge-sensing readout, and charge pumping.  Guided by these capabilities, we map out numerous milestones that progressively bridge the gap between Majorana zero-mode detection and long-term quantum computing applications.  These include (1) detecting non-Abelian anyon ‘fusion rules’ in two complementary schemes, one based on charge sensing, the other using a novel Majorana-mediated charge pump, (2) validation of a prototype topological qubit, (3) braiding to demonstrate non-Abelian statistics, and (4) observing the elusive topological phase transition accompanying the onset of Majorana modes.  With the exception of braiding, these proposed experiments require only a single wire with as few as two islands, a setup already available in the laboratory.  In the second part of the talk, I will introduce a new class of 2D microscopic models---termed ‘Majorana-dimer models’---which generalize well-known quantum dimer models by dressing the bosonic dimers with pairs of Majorana modes.  These models host a novel interacting topological phase of matter which has the same bulk anyonic content as the chiral Ising theory, albeit with a fully gapped edge.  These seemingly contradictory statements can be reconciled by noting that our phase is inherently fermionic:  it can be understood as the product of an Ising phase with a topological p-ip superconductor.  Potential physical realizations of this exotic state via a lattice of strongly interacting Majorana modes will be discussed.

In this talk, I would introduce spontaneous nematicity in the background of fractional quantum Hall fluids where symmetry breaking phenomenon intertwined with topological phase of matter. The resulting nematic FQH state is characterized by an order parameter that represents these quadrupolar fluctuations, which play the role of fluctuations of the local geometry of the quantum fluid. We demonstrate that the low-energy effective theory of the nematic order parameter has z=2 dynamical scaling exponent, due to a Berry phase term of the order parameter, which is related to the nondissipative Hall viscosity. By investigating the spectrum of collective excitations, we demonstrate that the mass gap of the Girvin-MacDonald-Platzman mode collapses at the isotropic-nematic quantum phase transition. An interesting feature of the nematic phase is that it has topological defects carrying nontrivial braiding statistics and fractional charge inherited from the topological fluid nature. In addition, I would also mention the decorated nodal line condensation in pair density wave SC, where the topological phase emerges concurrently with symmetry recovery by decorated defect condensation.